Calculate velocity magnitude, direction angle, x/y components, or speed from distance and time in m/s, km/h, mph, or ft/s online.

Output units

Magnitude of Velocity Formula

The following equation is used to calculate the Magnitude of Velocity.

Vm = SQRT(Vx² + Vy²)
a = atan2(Vy, Vx)
  • Where Vm is the velocity magnitude (m/s)
  • Vx is the x-component of velocity (m/s)
  • Vy is the y-component of velocity (m/s)
  • a is the direction from +X (degrees, counterclockwise, normalized to 0°–360°); direction is undefined at zero velocity

To calculate the magnitude of a velocity vector, square both the x- and y-components of velocity, add the results together, then finally take the square root of that value.

What is the Magnitude of Velocity?

Definition:

A magnitude of velocity measures the hypotenuse between the x and y components of velocity.

How to Calculate Magnitude of Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Magnitude of Velocity.

First, determine the x-component of velocity. In this example, the x-component of velocity is found to be 30 m/s.

Next, determine the y-component of velocity. For this problem, the y-component of velocity is found to be 50 m/s.

Finally, calculate the Magnitude of Velocity using the formula above:

Vm = SQRT( Vx^2 + Vy^2)

Vm = SQRT( 30^2 + 50^2)

Vm ≈ 58.3095 m/s